The H∞ control problem of a class of cyber-physical system (CPS) under malicious denial-of-service (DoS) jamming attack was researched, aiming at the influence of the DoS jamming attack on the CPS. An energy constrained DoS jammer with periodic attack strategy attacks the wireless channel in the CPS, decreasing the communication quality. Random packet dropouts caused by inherent factors exist in the wireless channel, and the DoS jammer’s attack strategy is unknown due to that DoS jamming attacks have the characteristics of suddenness and concealment. By expressing the influence of malicious DoS jamming attacks and the inherent factors in the wireless channel into a unified form and establishing an attack tolerance mechanism and an observer-based control strategy, sufficient conditions were obtained to guarantee the exponential mean square stability of the attacked CPS without knowing DoS jammer’s concrete attack strategy, and the prescribed H∞ performance index can be achieved simultaneously. The design of the H∞ controller is transformed into the solving of a convex optimization problem. Numerical simulations were used to demonstrate the correctness and effectiveness of the control strategy.
Mu-feng WANG,Bu-gong XU,Li-ding CHEN. H∞ control for cyber-physical system under periodic denial-of-service jamming attack. Journal of ZheJiang University (Engineering Science), 2019, 53(11): 2146-2153.
Fig.2Schematic diagram of working cycle of DoS jammer
Fig.3Norm of states for UPS using conventional control strategy
Fig.4Norm of states for UPS using H∞ control strategy
Fig.5Time of packet dropouts under DoS jamming attack
[1]
DERLER P, LEE E A, VINCENTELLIA S Modeling cyber-physical systems[J]. Proceedings of the IEEE, 2012, 100 (1): 13- 28
doi: 10.1109/JPROC.2011.2160929
[2]
KIM K D, KUMAR P R Cyber-physical systems: a perspective at the centennial[J]. Proceedings of the IEEE, 2012, 100 (13): 1287- 1308
[3]
JAZDI N. Cyber physical system in the context of industry 4.0 [C]// Proceedings of IEEE International Conference on Automation, Quality and Testing, Robotics. Cluj-Napoca: IEEE, 2014: 1?4.
[4]
LEE I, SOKOLSKY O, CHEN S J, et al Challenges and research directions in medical cyber-physical systems[J]. Proceedings of the IEEE, 2012, 100 (1): 75- 90
doi: 10.1109/JPROC.2011.2165270
[5]
MO Y L, KIM T H, BRANCIK K, et al Cyber-physical security of a smart gird infrastructure[J]. Proceedings of the IEEE, 2012, 100 (1): 195- 209
doi: 10.1109/JPROC.2011.2161428
[6]
LIU Y G, XU B G, DING Y H Convergence analysis of cooperative breaking control for interconnected vehicle systems[J]. IEEE Transactions on Intelligence Transport Systems, 2017, 18 (7): 1894- 1906
doi: 10.1109/TITS.2016.2615302
[7]
SAMPIGETHAYA K, POOVENDRAN R Aviation cyber-physical systems: foundations for future aircraft and air transport[J]. Proceedings of the IEEE, 2013, 101 (8): 1834- 1855
doi: 10.1109/JPROC.2012.2235131
[8]
FARWELL J P, ROHOZINSKI R Stuxnet and the future of cyber war[J]. Survival, 2011, 53 (1): 23- 40
doi: 10.1080/00396338.2011.555586
[9]
IASIELLO E. Cyber attack: a dull toll to shape foreign policy [C]// Proceedings of the International Conference on Cyber Conflict. Tallinn: IEEE, 2013: 1–18.
[10]
PETRENKO A S, PETRENKO S A, MAKOVEICHUK K A, et al. Protection model of PCS of subway from attacks type ?wanna cry?, ?petya? and ?bad rabbit? IoT [C]// Proceedings of the IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering. Moscow: IEEE, 2018: 945–949.
[11]
WOLF M, SERPANOS D Safety and security in cyber-physical systems and internet-of-things systems[J]. Proceedings of the IEEE, 2018, 106 (1): 9- 20
doi: 10.1109/JPROC.2017.2781198
[12]
TEIXEIRA A, PéREZ D, SANDBERG H, et al. Attack models and scenarios for networked control systems [C]// Proceedings of the 1st International Conference on High Conference Networked Systems. Beijing: ACM, 2012: 55–64.
[13]
CáRDENAS A A, AMIN S, SASTRY S. Secure control: towards survivable cyber-physical systems [C]// Proceedings of the 28th International Conference on Distributed Computing Systems Workshops. Beijing: IEEE, 2008: 495–500.
[14]
LEE P, CLARK A, BUSHNELL L, et al A passivity framework for modeling and mitigating wormhole attacks on networked control systems[J]. IEEE Transactions on Automatic Control, 2014, 59 (12): 3224- 3237
doi: 10.1109/TAC.2014.2351871
[15]
ZHANG H, CHENG P, SHI L, et al Optimal denial-of-service attack scheduling with energy constraint[J]. IEEE Transactions on Automatic Control, 2015, 60 (11): 3023- 3028
doi: 10.1109/TAC.2015.2409905
[16]
ZHANG H, CHENG P, SHI L, et al Optimal DoS attack scheduling in wireless networked control system[J]. IEEE Transactions on Control Systems Technology, 2016, 24 (3): 843- 852
doi: 10.1109/TCST.2015.2462741
[17]
FOROUSH S H, MART?NEZ S. On event-triggered control of linear systems under periodic denial of service attacks [C]// Proceedings of the 51st IEEE Annual Conference on Decision and Control. Maui: IEEE, 2012: 2551?2556.
[18]
DE PERSIS C, TESI P Input-to-state stabilizing control under denial-of-service[J]. IEEE Transactions on Automatic Control, 2015, 60 (11): 2930- 2944
doi: 10.1109/TAC.2015.2416924
[19]
DING K M, LI Y Z, QUEVEDO D E, et al Multi-channel transmission schedule for remote state estimation under DoS attacks[J]. Automatica, 2017, 78: 194- 201
doi: 10.1016/j.automatica.2016.12.020
[20]
LI Y Z, QUEVEDO D E, DEY S, et al SINR-based DoS attack on remote state estimation: a game-theoretic approach[J]. IEEE Transactions on Control of Network Systems, 2017, 4 (3): 632- 642
doi: 10.1109/TCNS.2016.2549640
[21]
ZHANG H, QI Y F, ZHOU H, et al Testing and defending methods against DoS attack in state estimation[J]. Asian Journal of Control, 2017, 19 (4): 1295- 1305
doi: 10.1002/asjc.1441
[22]
WANG Z D, HO D W C, LIU Y R, et al Variance-constrained filtering for uncertain stochastic systems with missing measurements[J]. IEEE Transactions on Automatic Control, 2003, 48 (7): 1254- 1258
doi: 10.1109/TAC.2003.814272
[23]
WU J, CHEN T W Design of networked control systems with packet dropouts[J]. IEEE Transactions on Automatic Control, 2007, 52 (7): 1314- 1319
doi: 10.1109/TAC.2007.900839
[24]
SASKIN A V, PETERSEN I R Robust filtering with missing data and a deterministic description of noise and uncertainty[J]. International Journal of Systems Science, 1997, 28 (4): 373- 390
doi: 10.1080/00207729708929397
[25]
FANG X S, WANG J C Stochastic observer-based guaranteed cost control for networked control systems with packet dropouts[J]. IET Control Theory and Applications, 2008, 2 (11): 980- 989
doi: 10.1049/iet-cta:20070379
[26]
WANG Z D, HO D W C, LIU Y R, et al Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements [J]. Automatica, 2009, 45 (3): 684- 691
doi: 10.1016/j.automatica.2008.10.025
[27]
XIONG J L, LAM J Stabilization of linear systems over networks with bounded packet loss[J]. Automatica, 2007, 43: 80- 87
doi: 10.1016/j.automatica.2006.07.017
[28]
TSE D, VISWANATH P. Fundamentals of wireless communication [M]. Cambridge: Cambridge University Press, 2005.
[29]
XU W Y, MA K, TRAPPE W, et al Jamming sensor networks: attack and defense strategies[J]. IEEE Network, 2006, 20 (3): 41- 47
doi: 10.1109/MNET.2006.1637931
[30]
LI M Y, KOUTSOPOULOS I, POOVENDRAN R Optimal jamming attack strategies and network defense policies in wireless sensor networks[J]. IEEE Transactions on Mobile Computing, 2010, 9 (8): 1119- 1133
doi: 10.1109/TMC.2010.75
[31]
OSANAIYE O, ALFA A S, HANCKE G P Statistical approach to detect jamming attacks in wireless sensor networks[J]. Sensors, 2018, 18 (6): 1691
doi: 10.3390/s18061691
[32]
PROAKIS J, SALEHI M. Digital communications [M]. New York: McGraw-Hill, 2007.
[33]
LI Y Z, SHI L, CHENG P, et al Jamming attacks on remote state estimation in cyber-physical systems: a game-theoretic approach[J]. IEEE Transactions on Automatic Control, 2015, 60 (10): 2831- 2836
doi: 10.1109/TAC.2015.2461851
[34]
YUAN Y, YUAN H H, GUO L, et al Resilient control of networked control system under DoS attacks: a unified game approach[J]. IEEE Transactions on Industrial Informatics, 2016, 12 (5): 1786- 1794
doi: 10.1109/TII.2016.2542208